On the radiation and diffraction of linear water waves by a rectangular structure over a sill. Part I. Infinite domain of finite water depth

Abstract

The effects of a bottom sill on the hydrodynamic coefficients, wave force, and reflection and transmission coefficients of a rectangular structure floating on the free surface are analyzed in this paper by use of a semi-analytical method. Linearized water wave theory and the method of separation of variables are applied to obtain analytical expressions for the diffracted and radiated wave potentials. The unknown coefficients in the obtained expressions are determined by use of the eigenfunction expansion matching method. To verify the obtained expressions and the proposed method, a comparison of the analytical results with those obtained by the boundary element method is made and very good agreement is achieved, which shows that the analytical expressions for the radiated and diffracted potentials are correct. By use of the present analytical solution, several results for the hydrodynamic coefficients, wave force, reflection and transmission coefficients are given.